## The Michigan Mathematical Journal

### Almost Gorenstein Rees Algebras of $p_{g}$-Ideals, Good Ideals, and Powers of the Maximal Ideals

#### Abstract

Let $(A,\mathfrak{m})$ be a Cohen–Macaulay local ring, and let $I$ be an ideal of $A$. We prove that the Rees algebra $\mathcal{R}(I)$ is an almost Gorenstein ring in the following cases:

(1) $(A,\mathfrak{m})$ is a two-dimensional excellent Gorenstein normal domain over an algebraically closed field $K\congA/\mathfrak{m}$, and $I$ is a $p_{g}$-ideal;

(2) $(A,\mathfrak{m})$ is a two-dimensional almost Gorenstein local ring having minimal multiplicity, and $I=\mathfrak{m}^{\ell}$ for all $\ell\ge1$;

(3) $(A,\mathfrak{m})$ is a regular local ring of dimension $d\ge2$, and $I=\mathfrak{m}^{d-1}$. Conversely, if $\mathcal{R}(\mathfrak{m}^{\ell})$ is an almost Gorenstein graded ring for some $\ell\ge2$ and $d\ge3$, then $\ell=d-1$.

#### Article information

Source
Michigan Math. J., Volume 67, Issue 1 (2018), 159-174.

Dates
Revised: 20 June 2017
First available in Project Euclid: 19 January 2018

https://projecteuclid.org/euclid.mmj/1516330972

Digital Object Identifier
doi:10.1307/mmj/1516330972

Zentralblatt MATH identifier
06965594

#### Citation

Goto, Shiro; Matsuoka, Naoyuki; Taniguchi, Naoki; Yoshida, Ken-ichi. Almost Gorenstein Rees Algebras of $p_{g}$ -Ideals, Good Ideals, and Powers of the Maximal Ideals. Michigan Math. J. 67 (2018), no. 1, 159--174. doi:10.1307/mmj/1516330972. https://projecteuclid.org/euclid.mmj/1516330972

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